Collision #1 - Bouncy Collision (one cart moving / one cart stationary)
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Blue solid line - Position for Cart A
Red solid line - Position for Cart B Blue dashed line - Velocity for Cart A Red dashed line - Velocity for Cart B Blue dotted line - Momentum for Cart A Red dotted line - Momentum for Cart B Green line - Total Momentum |
Calculations
Initial Momentum = Mass * Initial Velocity = 0.252 kg * 0.66 m/s = 0.16632 kg m/s
Final Momentum = Mass * Final Velocity = 0.252 kg * 0.6 m/s = 0.1512 kg m/s
Percent Difference = |.1512-.16632| / 0.16632 = 9.09%
Final Momentum = Mass * Final Velocity = 0.252 kg * 0.6 m/s = 0.1512 kg m/s
Percent Difference = |.1512-.16632| / 0.16632 = 9.09%
Conclusion
From this experiment, you can conclude that momentum is conserved. The initial and final momentum of the carts are 9.09% off, but this is a relatively small margin considering the numbers. This error margin could have come from slight inaccuracies with the best fit lines in Logger Pro as they are not completely accurate to the actual line.
Collision #2 - Bouncy Collision (both carts moving)
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Green solid line - Position for Cart A
Orange solid line - Position for Cart B Green dashed line - Velocity for Cart A Orange dashed line - Velocity for Cart B Green dotted line - Momentum for Cart A Orange dotted line - Momentum for Cart B Purple line - Total Momentum |
Calculations
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.32 m/s + 0.252 * -0.38= -0.01512 kg m/s
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.32 m/s + 0.252 * -0.38 = -0.0126 kg m/s
Percent Difference = |.0126-.01512| / 0.01512 = 16.67%
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.32 m/s + 0.252 * -0.38 = -0.0126 kg m/s
Percent Difference = |.0126-.01512| / 0.01512 = 16.67%
Conclusion
For this experiment, the percent difference is 16.67% which is moderately higher than the previous experiment. But you can still conclude that momentum is conserved because the values are very small so a slight difference is a large percent. You can see from the graph that the numbers are actually very close to each other. Velocity could also have been lost from small amounts of friction which would decrease the momentum we calculated.
Collision #3 - Sticky Collision (one cart moving / one cart stationary)
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Red solid line - Position for Cart A
Black solid line - Position for Cart B Red dashed line - Velocity for Cart A Black dashed line - Velocity for Cart B Red dotted line - Momentum for Cart A Black dotted line - Momentum for Cart B Orange line - Total Momentum |
Calculations
Initial Momentum = Mass B * Initial Velocity B = 0.252 kg * 0.43 m/s = 0.10836 kg m/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg )* 0.17 m/s = 0.08568 kg m/s
Percent Difference = |.08568-.10836| / 0.10836 = 20.93%
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg )* 0.17 m/s = 0.08568 kg m/s
Percent Difference = |.08568-.10836| / 0.10836 = 20.93%
Conclusion
This collision had a 20.93% difference between the final and initial momentum. Which is a large percent difference, but similar to the other experiments, both the initial and final momentum are very small values that are still very close to each other even if there is a large percent difference. This is shown in the graph. This percent error could have been caused by bad data being taken by the motion sensor as it picked up the velocity of the carts. Like the other experiments, friction is also a factor. We can assume that the momentum values are conserved if the experiment was repeated without friction.
Collision #4 - Sticky Collision (both carts moving)
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Orange solid line - Position for Cart A
Blue solid line - Position for Cart B Orange dashed line - Velocity for Cart A Blue dashed line - Velocity for Cart B Orange dotted line - Momentum for Cart A Blue dotted line - Momentum for Cart B Red line - Total Momentum |
Calculations
Initial Momentum = Mass A * Initial Velocity A + Mass B * Initial Velocity B = 0.252 kg * 0.18 m/s + 0.252 * -0.71= -0.13356 kg m/s
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg) * -0.22 m/s = -0.11088 kg m/s
Percent Difference = |-.11088 + .13356| /0.13356 = 16.98%
Final Momentum = (Mass A + Mass B) * Final Velocity A and B = (0.252 kg + 0.252 kg) * -0.22 m/s = -0.11088 kg m/s
Percent Difference = |-.11088 + .13356| /0.13356 = 16.98%
Conclusion
This experiment had a 16.98% percent difference, but like the other experiments, this percentage can be misleading as the values we are working with are very small, so any changes lead to larger percentage changes. When looking at the actual difference between the initial and final momentum, it is very small. You can assume that the momentum is conserved, but with possible sources of error coming from the motion sensor and/or friction.
Collision #5 - Explosion (neither cart moving, then both moving)
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Green solid line - Position for Cart A
Black solid line - Position for Cart B Green dashed line - Velocity for Cart A Black dashed line - Velocity for Cart B Green dotted line - Momentum for Cart A Black dotted line - Momentum for Cart B Orange line - Total Momentum |
Calculations
Initial Momentum = 0 kgm/s (neither cart is moving)
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.82m/s + 0.252 * -0.82 = 0 kgm/s
Percent Difference = 0%
Final Momentum = Mass A * Final Velocity A + Mass B * Final Velocity B = 0.252 kg * 0.82m/s + 0.252 * -0.82 = 0 kgm/s
Percent Difference = 0%
Conclusion
This experiment starts with the carts together and not moving. Then, the carts quickly move away from each other. Cart A had a velocity of 0.82 m/s and Cart B had a velocity of -0.82 m/s. The carts have identical velocities from start to end, which is why the percent difference is 0%. Therefore, you can conclude that the momentum is conserved in the system. There was initially no momentum because the two carts with the same mass are moving at the same velocity, and then cancel each other out.